Does this surgery really exist and why doesn't a doctor from here answer these types of questions? I wish to have one to remove an annoying brown spot in my sclera.
Yes it exists. No it is not normally done for pigmented spots that are not malignant. These spots are common in brown skin and black individuals. The cost is not covered if the reason is cosmetic. More can form and it can come back.
Any ophthalmic surgeon can do the procedure. Since what you are asking for is cosmetic surgery the surgeon would have to quote you a price based on the size and depth of the spot.